“The acceptance of the Epstein gifts involved a mistake of judgment,” Mr Reif said in a statement.

In an email published by the New York Times, Mr Ito told university provost Martin Schmidt that he had made the decision to step down “after giving the matter a great deal of thought over the past several days and weeks”.

He apologised an a separate email to members of the Lab, saying: “While this chapter is truly difficult, I am confident the lab will persevere.”

Mr Ito shared the emails with the New York Times, where he has served as a board member since 2012.

According to the New Yorker, internal MIT emails and documents show that, although Epstein was blacklisted from the university’s official donor database, Mr Ito and other Lab staff continued to accept contributions from him and actively tried to conceal where they came from.

Epstein was also allegedly consulted about the use of funds, and served as an intermediary between the Lab and other wealthy donors.

The New Yorker alleges that Epstein helped to secure at least $7.5m (£6.1m) in donations, including $2m from Microsoft founder Bill Gates.